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AI isn’t outthinking mathematicians, it’s out-remembering them

davidepiffer.com

331–340 of 545 posts

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#331
post #119
post #101

Earlier quoted context omitted.

Can LLMs not do this for you? Or would they go too far?

They add and add new code to the point when adding more is going to become very messy and then spagetti

What I was suggesting is to ask the LLM to compare function usage across files to identify overlap/redundancy.

The idea is to use the LLM to analyse the code base first before taking any action.

I think I'm suggesting a centaur approach.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#332
post #33

Yes. That's how LLMs do programming, mostly. It's also why LLMs don't need abstractions or parsimony as much as humans. They can work on something complicated without simplifying it first. This has major implications that haven't been fully realized yet. On the math side, there are long machine generated proofs. On the code side, there are high volumes of code with similar code not being folded into functions.

I've been working on generating a large code base for the last couple of weeks. Finally got around to generating a sort of code-duplication report and have spent the last week just having it de-duplicating logic that had been strewn all over the place (eg 11 different functions all doing date math to add x days to a date). dozens of items that had each been similar functions duplicated numerous times. crazy. (opus-5-…

LLMs love duplicating logic. Unfortunately they are not formal systems so we actually have to read their output

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#333
post #121
post #101

Earlier quoted context omitted.

Can LLMs not do this for you? Or would they go too far?

No, the problem is they're still really dumb, and lack the ability to make logical connections that are obvious to us. "should I walk or drive to the carwash" being a very recent example of the larger problem.

But they are very good at identifying patterns though. This task requires little logic IMO. So why not leverage LLM to perform redundancy analysis?

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#334

Sounds like another attempt to frame AI in a way that makes them feel better about themselves. The simpler explanation is that a working memory is a requirement for intelligence, and a larger working memory will make you more intelligent. Hence the AI can in fact be more intelligent than the mathematician.

Depends how you define intelligence. I struggle to consider LLMs actually intelligent, at least for any definition of intelligence that I would be content by.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#335

Earlier quoted context omitted.

I beg to differ because a compiler is deterministic.

Did you check? Do you care if it sometimes does mov ax, 0 or sometimes xor ax,ax? (Forgive my bad memory, it was a long time ago) Would you personally vouch, at your job, for the importance of proper assembly coding standards?

Yes, the same compiler generates the same output given the same input. I'd be willing to put a large amount of money on that result.

I read a lot of assembly.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#336

It was duuring my PhD I realised that thinking is essentially 1. remembering all the different information to remember all the tricks 2. trying all the different tricks in the problem 3. optimizing deciding which to try based on different information 4. trying random things to discover patterns (and hence new tricks) 5. explaining your tricks to others so that they can do the first 4 steps independently and come up w…

> That's all thinking is

That's more because a PhD (especially in this socioeconomic era where academia is also a microcosm of capitalism) does not automatically teach or focus on deep inquiry, rather narrow research programmes. Case in point, fallaciously reducing it all to a superficial theory of tricks means that by the same light, general relativity or any other major scientific result is merely just a trick. That framing ought to be absurd on the face of it but the fact is many PhD students do still graduate with very unexamined understanding of science, cognition, philosophy, etc. (Another way to see this is to note how such an argument is letting the notion of "trick"/"heuristic" do all the heavy lifting--something an advanced education should have nurtured the critical thinking skills to avoid that very metacognitive pitfall in the first place, which is ironic.) (Yet another way is to see how increasingly experts of one field or another insist that one must stay on their lane when speaking about a complex topic.) There are professors and thinkers who have written/spoken about this but they are a minority. Even Einstein himself when he complained that more and more scientists were trained/structured to miss the forest for the trees, and that was almost 100 years ago.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#337
post #314

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

> Combine A + B Really, compress. Compression is a useful proxy for intelligence. To compress data efficiently, an entity must discover the underlying patterns, structures, and regularities within that data. Identifying these structures is precisely what we define as "understanding" or "intelligence. Anything we put into writing can be thought of as a string of data. The Kolmogorov complexity of a string of data is t…

I feel like we also miss something related to #2 (Discipline). I never needed discipline to sit at a computer coding as a kid for hours on end — if anything I’d have needed massive discipline to NOT do it.

I wonder if what we call discipline (and the resulting skill that we call talent) is really just insanely strong and aligned interest.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#338

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

Human can have periods of heightened mental capacity. Sometimes I looked back at some of my work days or weeks later and amazed how I could have done it. When you're in the flow, have enough sleep, and have long period of non-interrupted time, you can do amazing work.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#339

Earlier quoted context omitted.

So, you're willing to claim that a conclusion that you don't understand the reasoning for is equivalent to comprehension? Because, again, I can point to hundreds of examples of texts where nobody but the author understands it, and they're only giving summarized "commandments" that you should follow if you want good results. If I told you "don't use spin locks, call futex instead", do you think have gained an understa…

If I told you "don't use spin locks, call futex instead", do you think have gained an understanding of the Linux scheduler? Yes, because I already knew what schedulers are, what spinlocks are, and if I want to know what futex is I can go look it up. Comprehension is within my grasp. Your original claim, which you’ve repeatedly distanced yourself from (by trying to use comprehensible examples) but won’t admit to, was…

Bullshit. Human comprehension will not continue, it will reduced to "when the AI tells us to add Bismuth, strontium, and copper together in this way, we get a superconductor", but that doesn't mean we understand high temperature superconductivity.

For what it's worth, we've known about BSCCO for nearly 40 years, and we still don't have a great physical understanding of how it works, thought we made decent progress in 2022.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#340

I often think “what will ‘maintainable’ code look like in the future?” given this kind of thing. Much of ‘good coding’ is about optimising the codebase for workability for a human intellect with human working memory. Though having said that, from the studies I’ve come across it seems like LLMs tend to generate more verbose code but perform better over the long-term when the code is maintained and not allowed to spraw…

Is this assuming or studying human maintenance?
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